Games are more forgiving.
-Saving around every corner and before/after every challenge.
-You can take more hits before you die.
-3D makes platform jumping a bit easier to fail at, they compensate with bigger platforms and characters latching onto edges.
-If you die, you just need to replay 5 minutes or so, rather than the entire game.
-Hit the glowing spot.
-If you can't figure the above out, the game tells you to hit the glowing spot.
Other than that, access to the internet has made games a lot easier;
-If you're stuck, there's youtube.
-If you're still stuck, google for a guide.
-Before the game is even out, people will post every possible glitch and exploit for invincibility or an extremely easy time online.
And of course there are a lot of games that "rely heavily on/are designed for multiplayer". Those games only have a singleplayer campaign to kill some time when your internet is down.
...
Achievements and Trophies were added to give replay value to games that have no replay value of their own. If you really need a 'locked' Icon to tell you to go challenge yourself, it means the game isn't challenging you.
And there are plenty of achievement/trophy guides as well.